{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VOWTII5EBUZ4JQJMER2THWTNEK","short_pith_number":"pith:VOWTII5E","canonical_record":{"source":{"id":"1908.07595","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-20T20:21:41Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"2512e730287a3a7f9abda55cd27793f644f3eec268051633015b781730201d2f","abstract_canon_sha256":"554602dc0a7d77c65a1f647488aa4d3165a4327c176e2a90d8976b5320e35a0b"},"schema_version":"1.0"},"canonical_sha256":"abad3423a40d33c4c12c247533da6d228da5f273c3e2bf62331ea4d3798b0502","source":{"kind":"arxiv","id":"1908.07595","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07595","created_at":"2026-07-04T23:59:34Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07595v2","created_at":"2026-07-04T23:59:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07595","created_at":"2026-07-04T23:59:34Z"},{"alias_kind":"pith_short_12","alias_value":"VOWTII5EBUZ4","created_at":"2026-07-04T23:59:34Z"},{"alias_kind":"pith_short_16","alias_value":"VOWTII5EBUZ4JQJM","created_at":"2026-07-04T23:59:34Z"},{"alias_kind":"pith_short_8","alias_value":"VOWTII5E","created_at":"2026-07-04T23:59:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VOWTII5EBUZ4JQJMER2THWTNEK","target":"record","payload":{"canonical_record":{"source":{"id":"1908.07595","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-20T20:21:41Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"2512e730287a3a7f9abda55cd27793f644f3eec268051633015b781730201d2f","abstract_canon_sha256":"554602dc0a7d77c65a1f647488aa4d3165a4327c176e2a90d8976b5320e35a0b"},"schema_version":"1.0"},"canonical_sha256":"abad3423a40d33c4c12c247533da6d228da5f273c3e2bf62331ea4d3798b0502","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:59:34.906205Z","signature_b64":"8teKnrX0/4CHagkOA0Dswlo6H8u3/WjSyofb3lAmebk8wrqpH3ceqvHrgHKv2nxX3r4Su4WLjzZ0UYZZ2L6HAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abad3423a40d33c4c12c247533da6d228da5f273c3e2bf62331ea4d3798b0502","last_reissued_at":"2026-07-04T23:59:34.905778Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:59:34.905778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.07595","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T23:59:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Yz+TANS6CVuN7S9PJceAGEWsu1j4w13IppDbgbekjQcZlcJv4a0CDDDu4Gr9SfNurJyCrdP0f0ybcGuiXkuDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:12:37.356383Z"},"content_sha256":"026f7810121facea3a60de527badfce2e981f188ad1e853b8815abef87b6115e","schema_version":"1.0","event_id":"sha256:026f7810121facea3a60de527badfce2e981f188ad1e853b8815abef87b6115e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VOWTII5EBUZ4JQJMER2THWTNEK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Connection probabilities in the double-dimer model -- the case of two connectivity patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Nahid Ghodratipour, Shahin Rouhani","submitted_at":"2019-08-20T20:21:41Z","abstract_excerpt":"We apply the Grassmannian representation of the dimer model, an equivalent approach to Kasteleyn's solution to the close-packed dimer problem, to calculate the connection probabilities for the double-dimer model with wired/free/wired/free boundary conditions, on a rectangular subdomain of the square lattice with four marked boundary points at the corners. Using some series identities related to Schwarz-Christoffel transformations, we show that the continuum of the result is consistent with the corresponding one in the upper half-plane (previously obtained by Kenyon-Wilson), which is in turn id"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07595","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07595/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T23:59:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DacLLNoCqCOyTTjS46iPSZ3RYcDgwq28MJOeZATbaJRwr/ARKA+yTJ1xYGLwkToD1Krb1Zobvq9PyY95kR0ACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:12:37.359778Z"},"content_sha256":"ebf9a9a0260c205a62050c5ae0f7eccaa26409f1c37de31a330a6c3e9d543ae4","schema_version":"1.0","event_id":"sha256:ebf9a9a0260c205a62050c5ae0f7eccaa26409f1c37de31a330a6c3e9d543ae4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VOWTII5EBUZ4JQJMER2THWTNEK/bundle.json","state_url":"https://pith.science/pith/VOWTII5EBUZ4JQJMER2THWTNEK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VOWTII5EBUZ4JQJMER2THWTNEK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T10:12:37Z","links":{"resolver":"https://pith.science/pith/VOWTII5EBUZ4JQJMER2THWTNEK","bundle":"https://pith.science/pith/VOWTII5EBUZ4JQJMER2THWTNEK/bundle.json","state":"https://pith.science/pith/VOWTII5EBUZ4JQJMER2THWTNEK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VOWTII5EBUZ4JQJMER2THWTNEK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VOWTII5EBUZ4JQJMER2THWTNEK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"554602dc0a7d77c65a1f647488aa4d3165a4327c176e2a90d8976b5320e35a0b","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-20T20:21:41Z","title_canon_sha256":"2512e730287a3a7f9abda55cd27793f644f3eec268051633015b781730201d2f"},"schema_version":"1.0","source":{"id":"1908.07595","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07595","created_at":"2026-07-04T23:59:34Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07595v2","created_at":"2026-07-04T23:59:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07595","created_at":"2026-07-04T23:59:34Z"},{"alias_kind":"pith_short_12","alias_value":"VOWTII5EBUZ4","created_at":"2026-07-04T23:59:34Z"},{"alias_kind":"pith_short_16","alias_value":"VOWTII5EBUZ4JQJM","created_at":"2026-07-04T23:59:34Z"},{"alias_kind":"pith_short_8","alias_value":"VOWTII5E","created_at":"2026-07-04T23:59:34Z"}],"graph_snapshots":[{"event_id":"sha256:ebf9a9a0260c205a62050c5ae0f7eccaa26409f1c37de31a330a6c3e9d543ae4","target":"graph","created_at":"2026-07-04T23:59:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.07595/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We apply the Grassmannian representation of the dimer model, an equivalent approach to Kasteleyn's solution to the close-packed dimer problem, to calculate the connection probabilities for the double-dimer model with wired/free/wired/free boundary conditions, on a rectangular subdomain of the square lattice with four marked boundary points at the corners. Using some series identities related to Schwarz-Christoffel transformations, we show that the continuum of the result is consistent with the corresponding one in the upper half-plane (previously obtained by Kenyon-Wilson), which is in turn id","authors_text":"Nahid Ghodratipour, Shahin Rouhani","cross_cats":["cond-mat.stat-mech","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-20T20:21:41Z","title":"Connection probabilities in the double-dimer model -- the case of two connectivity patterns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07595","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:026f7810121facea3a60de527badfce2e981f188ad1e853b8815abef87b6115e","target":"record","created_at":"2026-07-04T23:59:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"554602dc0a7d77c65a1f647488aa4d3165a4327c176e2a90d8976b5320e35a0b","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-20T20:21:41Z","title_canon_sha256":"2512e730287a3a7f9abda55cd27793f644f3eec268051633015b781730201d2f"},"schema_version":"1.0","source":{"id":"1908.07595","kind":"arxiv","version":2}},"canonical_sha256":"abad3423a40d33c4c12c247533da6d228da5f273c3e2bf62331ea4d3798b0502","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abad3423a40d33c4c12c247533da6d228da5f273c3e2bf62331ea4d3798b0502","first_computed_at":"2026-07-04T23:59:34.905778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:34.905778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8teKnrX0/4CHagkOA0Dswlo6H8u3/WjSyofb3lAmebk8wrqpH3ceqvHrgHKv2nxX3r4Su4WLjzZ0UYZZ2L6HAw==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:34.906205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07595","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:026f7810121facea3a60de527badfce2e981f188ad1e853b8815abef87b6115e","sha256:ebf9a9a0260c205a62050c5ae0f7eccaa26409f1c37de31a330a6c3e9d543ae4"],"state_sha256":"5bf2142028fc779e19136d807bdfeeafb2d4ab8e8c91cb3a6337a9c035075189"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eP0lRB0HLZNU4DWNn2UMbKmq+jhTMRJbRM10pRuiyjYdjfcJsVMjqj4HGEhFbRmXsfc6v/GYd2hjZgVbQwgLBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T10:12:37.389079Z","bundle_sha256":"0461e8446fe9e51c99a7c7fcdd260cfa955a8ceef8d887e6f894f6ff2ea91bb9"}}